Determining how well a group of satellites cover a planet is a critical component of constellation design. Usually some minimum number of satellites must be visible to every point in the region of interest in order to satisfy the mission. A prime example is that of a cellular telephone satellite system. In order to provide worldwide coverage at every instant of time, at least one satellite must be visible to every point of the earth with an elevation greater than some minimum limit. From a constellation designer's point of view, the goal is to determine the minimum number of satellites required to satisfy the mission constraints. The fewer the number of satellites, the lower the cost of the entire constellation.
Classically, this optimization problem was solved using a brute force, planetary frame of reference approach. For example, if the goal is to provide worldwide single satellite coverage with n satellites, such that every ground point on the surface of the planet saw at least one satellite at an elevation of 15.degree. or higher the method would be as follows.
The planet's surface is divided into a grid of latitude/longitude points at some degree of resolution (say 10.degree.). The process is started at one latitude/longitude point. The orbit of one of n satellites is propagated over the period of interest checking (and retaining) the visibility of the one satellite over time. This is repeated for all n satellites. The next adjacent latitude/longitude point is advanced and the process is repeated for all n satellites until the entire grid has been evaluated. Assuming, for example, n=24 and a 24 hour time period of interest at 1 minute time steps then a total of [1440 time steps*24 satellites*(36*18) latitude/longitude points=2.24e07] visibility calculations have to be performed. Obviously, as more satellites are added, grid density is increased, and constraints are added, the computational burden grows geometrically.
This classic approach has the advantage of being simple to implement and test, but the disadvantage of being extremely slow as more satellites are added. With the advent of satellite systems such as Iridium (66 satellites) it has become necessary to develop a coverage algorithm that gives results in a reasonable amount of time.